Hi, Patrick,
I agree with you that the UID is saved somewhere, but the address is not open to public, neither reference manual nor data sheet mentions the UID address for the LPC15xx.
For the LPC5410x, because the ISP commend has issue, so the errata gives the address of UID. But both RM and data sheet of LPC5410x do not mention the UID address officially.
BR
XiangJun Rong